Problem: Simplify the following expression and state the condition under which the simplification is valid: $p = \dfrac{x^2 - 16}{x^2 - 4x}$
First factor the expressions in the numerator and denominator. $ \dfrac{x^2 - 16}{x^2 - 4x} = \dfrac{(x + 4)(x - 4)}{(x)(x - 4)} $ Notice that the term $(x - 4)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(x - 4)$ gives: $p = \dfrac{x + 4}{x}$ Since we divided by $(x - 4)$, $x \neq 4$. $p = \dfrac{x + 4}{x}; \space x \neq 4$